GAGrasp: Geometric Algebra Diffusion for Dexterous Grasping

TL;DR

GAGrasp tackles dexterous grasp generation under diverse object poses by enforcing $SE(3)$ equivariance through a geometric algebra (GA) backbone within a diffusion framework. It combines a symmetry-aware, GA-based diffusion model with a differentiable physics-informed refinement layer to produce physically plausible, stable grasps across out-of-distribution poses. The approach demonstrates improved data and parameter efficiency, robustness to pose variations, and enhanced grasp stability and diversity, outperforming baseline diffusion and VAE-based methods. This work advances practical robotic manipulation by embedding symmetry directly into the learning architecture and coupling it with differentiable physics for reliable grasp synthesis in real-world environments.

Abstract

We propose GAGrasp, a novel framework for dexterous grasp generation that leverages geometric algebra representations to enforce equivariance to SE(3) transformations. By encoding the SE(3) symmetry constraint directly into the architecture, our method improves data and parameter efficiency while enabling robust grasp generation across diverse object poses. Additionally, we incorporate a differentiable physics-informed refinement layer, which ensures that generated grasps are physically plausible and stable. Extensive experiments demonstrate the model's superior performance in generalization, stability, and adaptability compared to existing methods. Additional details at https://gagrasp.github.io/

Figures (5)

• Figure 1: Symmetries in robotic grasping. The figure shows how our model leverages $SE(3)$ symmetries. Starting with an object observation $O$, the model generates a grasp $\mathbf{g}$. After an $SE(3)$ transformation to $O'$, the probability of generating the corresponding transformed grasp $\mathbf{g}'$ remains invariant: $P(\mathbf{g}|O) = P(\mathbf{g}'|O')$.
• Figure 2: Overview of the GAGrasp architecture. The point cloud $O$ and grasp configuration $g_t$ are embedded using $\mathbb{G}_{3,0,1}$, processed through GATr blocks ensuring $SE(3)$ equivariance, with down-sampling to enhance efficiency. A cross-attention mechanism uses the embedded grasp and diffusion step $t$ to predict the updated grasp $g_{t-1}$.
• Figure 3: The GATr Block processes key, value, and query inputs with equivariant layers, using geometric algebra-based attention and nonlinearities to maintain $SE(3)$ equivariance of the grasp configuration.
• Figure 4: Experimental Results. Grasp success rate and diversity metrics across different data amounts. "Ours w/ opt" refers to our model with the physics-informed refinement layer. Left: Our model outperforms others in grasp success rate, especially with fewer training samples. Middle: Our model generates more diverse grasps. Right: Our method is robust to out-of-distribution data with random $SE(3)$ transformations.
• Figure 5: Example Grasps Generated by our Method. Our model generates stable grasps for unseen objects. As the physics-informed refinement weight $\lambda$ increases (left to right), the model produces more stable power grasps, while a smaller $\lambda$ results in precision fingertip grasps, showing adaptability in grasp types.